Kate Middleton and Prince William couldn't wait to meet Prince Harry's new girlfriend Meghan Markle and really liked the "Suits" alum after their first meeting.

In a new book "Royals at War," investigative journalists Dylan Howard and Andy Tillett have claimed that Kate Middleton and Prince William were desperate to meet Meghan Markle. And though they really liked Meghan as a person, they were concerned that things were moving too fast with her and Prince Harry, reports Mail Online.

According to the book, William asked his younger brother if Meghan is "the right one?" after the meeting, which didn't go down well with Harry. The book also says that Kate was also worried about the relationship, and took her brother-in-law to one side to express her concerns after meeting his new love at Kensington Palace.

"She (Kate) gently reminded him that he was dating someone with a completely different life, past, and career and it would take time, care and attention for them to integrate," the pair wrote in the book.

The journalists also noted that Kate's concerns didn't stem from any worries about Meghan as a person - but simply the speed at which things were moving. Harry and Meghan started dating in 2016 and tied the knot after two years in May 2018, welcoming their son Archie in 2019.

Dyland and Andy also claimed that the feud could have been avoided if "Harry had been able to empathise and take his brother's concerns in the spirit they were intended," noting that the royal feels extra protective of his wife because of what happened with her mother Princess Diana.

"It's my opinion that Harry feels he couldn't protect his mother, so he's going all out to protect his wife. He is so sensitive he often sees criticism or negativity where there isn't any," a source stated for the book.

The Sussexes had themselves also discussed Meghan's meeting with William and Kate during their engagement interview. When asked what it was like introducing his then-fiance to his father Prince Charles and brother William, Harry had said: "What was it like? It was exciting I mean I've - you know I'd been seeing her for a period of time when I - literally didn't tell anybody at all. And then William was longing to meet her and so was Catherine."

royal christmas
Princess Beatrice, Princess Eugenie, Princess Anne, Princess Royal, Prince Andrew, Duke of York, Prince William, Duke of Cambridge, Catherine, Duchess of Cambridge, Meghan Markle and Prince Harry attend Christmas Day Church service at Church of St Mary Magdalene on 25 December 2017 in King's Lynn, England. Chris Jackson/Getty Images

"So, you know, being our neighbours we managed to get that in a couple of - well quite a few times now and Catherine has been absolutely...," the 35-year-old said, to which Meghan added: "She's been wonderful." Harry then continued: "...amazing, as has William as well, you know, fantastic support."